If the angles are such that 2x + y = 180, this means that two angles are equal and our triangle is isosceles. However, there are two cases depending on which angles are equal:

case 1) sides RQ and RS are equal and the perimeter is 7+7+4 = 18 -> answer A

case 2) sides SQ and SR are equal and the perimeter is 4+4+7 = 15 -> answer B

Since we can't say which one is greater than the other, the answer is D

The word problem implicates that the given triangle is an isosceles triangle. So the third side can be either 7 or 4. So substituting both the values would give 15 or 18. So precisely finding bigger number is not easy.

TRAP: Images can be misleading. Don't fall for them. Read question carefully and then have an imaginary figure based on information.

I picked D

The trap in this question: To trick you to think about only about one of the cases:
Case 1: P = 4 + 4 + 7 = 15
Case 2: P = 4 + 7 + 7 = 18

Answer is D.
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